I'm trying to understand a slide from my notes. I do understand what we're trying to do but not why we are doing it. Basically why are we expanding F so that each term has a B? After the "now compare with:" line where did we get that equation from? Also why are we setting the I0 to 1, the I1 to 0 and the I2 and I3 to C?

Could someone please explain this, the slide is from my notes which I have uploaded to tinypic for viewing.

i50.tinypic.com/zl3iqd.jpg

Thanks for any help.

 

A & B are the control lines to the MUX so every possibility of A, B, C (all 8 of them) should contain A & B terms so that they can control the MUX.

Recall how the select lines (A & B) choose an input line to pass to the output. There are 2 select lines, therefore \(2^2 = 4\) input lines.

For each possible input for A, B, & C, what should the output be? (Draw a truth table).

The inputs to a n-input MUX are typically labeled \(I_0, \: I_1, \: I_2, \: ... , \: I_{n-1}\) where input \(I_0\) is selected by setting the select lines to 0, 0. Input \(I_1\) is selected by setting the select lines to 0, 1, etc.